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ЧМ ЛР7

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x = 0:0.01:1;

y(1) = 1;

h = x(2)-x(1);

for i = 1:1:length(x)-1

y(i+1) = y(i)+h*x(i)^2;

end

y1 = x.^3/3+1;

e = abs(y-y1)

e = 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0007 0.0007 0.0008 0.0008 0.0008 0.0009 0.0009 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0014 0.0014 0.0015 0.0016 0.0016 0.0017 0.0017 0.0018 0.0019 0.0019 0.0020 0.0020 0.0021 0.0022 0.0022 0.0023 0.0024 0.0024 0.0025 0.0026 0.0027 0.0027 0.0028 0.0029 0.0030 0.0030 0.0031 0.0032 0.0033 0.0033 0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.0039 0.0040 0.0041 0.0042 0.0043 0.0044 0.0045 0.0046 0.0047 0.0048 0.0049 0.0050

Аналитически:

>> test

T =

0

0.0000

0.0000

0.0000

0.0000

0.0000

0.0001

0.0001

0.0001

0.0002

0.0004

0.0005

0.0006

0.0013

0.0019

0.0025

0.0031

0.0063

0.0094

0.0126

0.0157

0.0314

0.0471

0.0628

0.0785

0.1440

0.2096

0.2751

0.3406

0.4056

0.4705

0.5354

0.6003

0.6628

0.7252

0.7877

0.8502

0.9136

0.9770

1.0405

1.1039

1.1633

1.2226

1.2819

1.3413

1.4032

1.4651

1.5270

1.5888

1.6453

1.7017

1.7582

1.8146

1.8793

1.9439

2.0085

2.0732

2.1344

2.1957

2.2569

2.3182

2.3917

2.4653

2.5388

2.6124

2.6843

2.7563

2.8282

2.9002

2.9694

3.0386

3.1078

3.1770

3.2462

3.3154

3.3847

3.4539

3.5184

3.5829

3.6474

3.7119

3.7643

3.8167

3.8691

3.9215

3.9816

4.0418

4.1020

4.1622

4.2368

4.3114

4.3860

4.4606

4.5311

4.6016

4.6721

4.7426

4.8131

4.8836

4.9541

5.0245

5.0870

5.1494

5.2118

5.2742

5.3377

5.4011

5.4646

5.5280

5.6082

5.6884

5.7685

5.8487

5.9467

6.0447

6.1427

6.2407

6.3503

6.4599

6.5695

6.6791

6.7874

6.8957

7.0040

7.1124

7.2134

7.3145

7.4155

7.5166

7.6008

7.6850

7.7693

7.8535

7.9270

8.0004

8.0739

8.1474

8.2092

8.2711

8.3329

8.3948

8.4627

8.5307

8.5987

8.6667

8.7449

8.8231

8.9013

8.9795

9.0668

9.1542

9.2416

9.3289

9.4290

9.5290

9.6290

9.7290

9.8311

9.9333

10.0355

10.1376

10.2393

10.3410

10.4427

10.5444

10.6304

10.7163

10.8022

10.8881

10.9645

11.0409

11.1172

11.1936

11.2600

11.3265

11.3929

11.4594

11.5234

11.5874

11.6514

11.7154

11.7908

11.8662

11.9416

12.0171

12.1011

12.1851

12.2691

12.3531

12.4476

12.5422

12.6368

12.7314

12.8395

12.9476

13.0558

13.1639

13.2695

13.3752

13.4808

13.5865

13.6755

13.7646

13.8537

13.9428

14.0215

14.1001

14.1788

14.2575

14.3269

14.3964

14.4658

14.5353

14.5950

14.6548

14.7145

14.7743

14.8307

14.8871

14.9436

15.0000

Y =

1.0000 0

1.0000 -0.0001

1.0000 -0.0001

1.0000 -0.0002

1.0000 -0.0002

1.0000 -0.0005

1.0000 -0.0007

1.0000 -0.0010

1.0000 -0.0012

1.0000 -0.0025

1.0000 -0.0037

1.0000 -0.0050

1.0000 -0.0062

1.0000 -0.0125

1.0000 -0.0188

1.0000 -0.0250

1.0000 -0.0312

0.9998 -0.0623

0.9996 -0.0932

0.9992 -0.1239

0.9988 -0.1543

0.9952 -0.3033

0.9893 -0.4467

0.9812 -0.5843

0.9710 -0.7161

0.9075 -1.1995

0.8160 -1.5715

0.7040 -1.8304

0.5787 -1.9802

0.4479 -2.0285

0.3170 -1.9874

0.1915 -1.8698

0.0758 -1.6895

-0.0231 -1.4703

-0.1073 -1.2203

-0.1752 -0.9527

-0.2261 -0.6791

-0.2605 -0.4059

-0.2779 -0.1478

-0.2797 0.0870

-0.2675 0.2924

-0.2452 0.4542

-0.2142 0.5841

-0.1765 0.6812

-0.1341 0.7458

-0.0866 0.7801

-0.0381 0.7830

0.0097 0.7578

0.0552 0.7085

0.0935 0.6461

0.1279 0.5707

0.1577 0.4859

0.1826 0.3951

0.2047 0.2875

0.2198 0.1806

0.2281 0.0782

0.2301 -0.0163

0.2265 -0.0967

0.2184 -0.1663

0.2064 -0.2239

0.1912 -0.2693

0.1699 -0.3076

0.1464 -0.3289

0.1219 -0.3347

0.0975 -0.3271

0.0746 -0.3089

0.0532 -0.2827

0.0340 -0.2509

0.0172 -0.2159

0.0035 -0.1812

-0.0079 -0.1473

-0.0170 -0.1157

-0.0240 -0.0875

-0.0292 -0.0635

-0.0329 -0.0441

-0.0354 -0.0297

-0.0371 -0.0202

-0.0382 -0.0154

-0.0391 -0.0142

-0.0401 -0.0162

-0.0413 -0.0206

-0.0425 -0.0257

-0.0440 -0.0317

-0.0458 -0.0383

-0.0480 -0.0452

-0.0510 -0.0531

-0.0544 -0.0606

-0.0583 -0.0672

-0.0625 -0.0728

-0.0681 -0.0778

-0.0740 -0.0805

-0.0801 -0.0807

-0.0860 -0.0783

-0.0914 -0.0738

-0.0964 -0.0674

-0.1008 -0.0592

-0.1047 -0.0495

-0.1078 -0.0386

-0.1101 -0.0270

-0.1116 -0.0148

-0.1122 -0.0025

-0.1120 0.0084

-0.1112 0.0190

-0.1096 0.0293

-0.1075 0.0390

-0.1047 0.0482

-0.1014 0.0567

-0.0976 0.0645

-0.0932 0.0715

-0.0872 0.0792

-0.0806 0.0857

-0.0735 0.0911

-0.0660 0.0954

-0.0564 0.0995

-0.0465 0.1024

-0.0364 0.1043

-0.0261 0.1054

-0.0145 0.1059

-0.0029 0.1056

0.0086 0.1045

0.0199 0.1028

0.0310 0.1003

0.0417 0.0969

0.0519 0.0926

0.0617 0.0873

0.0702 0.0814

0.0781 0.0745

0.0852 0.0668

0.0915 0.0583

0.0961 0.0506

0.1001 0.0424

0.1033 0.0338

0.1057 0.0249

0.1073 0.0170

0.1082 0.0089

0.1086 0.0007

0.1083 -0.0075

0.1077 -0.0143

0.1066 -0.0211

0.1051 -0.0278

0.1031 -0.0344

0.1005 -0.0414

0.0975 -0.0483

0.0940 -0.0549

0.0900 -0.0612

0.0850 -0.0680

0.0794 -0.0745

0.0734 -0.0804

0.0668 -0.0858

0.0591 -0.0913

0.0509 -0.0960

0.0424 -0.1000

0.0335 -0.1032

0.0230 -0.1060

0.0123 -0.1077

0.0015 -0.1083

-0.0093 -0.1079

-0.0203 -0.1064

-0.0310 -0.1037

-0.0414 -0.1001

-0.0514 -0.0954

-0.0608 -0.0897

-0.0696 -0.0830

-0.0777 -0.0756

-0.0850 -0.0674

-0.0905 -0.0599

-0.0953 -0.0519

-0.0994 -0.0435

-0.1027 -0.0349

-0.1051 -0.0269

-0.1068 -0.0188

-0.1080 -0.0106

-0.1084 -0.0023

-0.1084 0.0049

-0.1078 0.0121

-0.1068 0.0193

-0.1052 0.0263

-0.1033 0.0330

-0.1010 0.0396

-0.0983 0.0459

-0.0951 0.0521

-0.0909 0.0592

-0.0862 0.0659

-0.0810 0.0722

-0.0754 0.0781

-0.0685 0.0841

-0.0612 0.0896

-0.0535 0.0944

-0.0454 0.0985

-0.0359 0.1024

-0.0261 0.1053

-0.0160 0.1073

-0.0058 0.1083

0.0059 0.1083

0.0176 0.1070

0.0290 0.1045

0.0401 0.1007

0.0505 0.0959

0.0604 0.0901

0.0695 0.0832

0.0779 0.0755

0.0843 0.0682

0.0900 0.0605

0.0951 0.0522

0.0993 0.0436

0.1025 0.0356

0.1049 0.0275

0.1068 0.0191

0.1079 0.0107

0.1084 0.0032

0.1084 -0.0044

0.1078 -0.0119

0.1067 -0.0193

0.1054 -0.0257

0.1037 -0.0319

0.1016 -0.0381

0.0991 -0.0441

0.0965 -0.0496

0.0935 -0.0550

0.0903 -0.0602

0.0867 -0.0652

[T1 Y1] = ode45('oscil',[0 15],[1;0]);

[T2 Y2] = ode23('oscil',[0 15],[1;0]);

plot(T1,Y1(:,1))

grid on

hold on

plot(T1,Y1(:,2))

title('ode45')

legend('y1','y2')

figure

plot(T2,Y2(:,1))

grid on

hold on

plot(T2,Y2(:,2))

legend('y1','y2')

title('ode23')

>> t = 0:0.0001:15;

>> y = (exp(-t).*(87*cos(3*t)+26*sin(3*t))+(9*sin(t)-2*cos(t)))/85;

>> dy = (9*cos(t))/85 + (2*sin(t))/85 - (87*cos(3*t) + 26*sin(3*t))./(85*exp(t)) + (78*cos(3*t) - 261*sin(3*t))./(85*exp(t));

>> plot(t,y)

hold on

grid on

>> plot(t,dy)

>> y = [log(0.01) 1/0.01];

>> [T1 Y1] = ode45('oscil',[0.01 5],y)

T1 =

0.0100

0.0105

0.0110

0.0115

0.0120

0.0142

0.0163

0.0185

0.0207

0.0241

0.0274

0.0308

0.0342

0.0399

0.0456

0.0513

0.0569

0.0664

0.0758

0.0852

0.0947

0.1101

0.1255

0.1409

0.1563

0.1808

0.2053

0.2299

0.2544

0.2791

0.3039

0.3286

0.3534

0.3781

0.4029

0.4276

0.4524

0.4771

0.5019

0.5266

0.5514

0.5761

0.6009

0.6256

0.6504

0.6751

0.6999

0.7246

0.7494

0.7741

0.7989

0.8236

0.8484

0.8731

0.8979

0.9226

0.9474

0.9605

0.9737

0.9868

1.0000

Y1 =

-4.6052 100.0000

-4.5562 95.2163

-4.5094 90.8698

-4.4648 86.9028

-4.4221 83.2673

-4.2565 70.5256

-4.1146 61.2076

-3.9904 54.0770

-3.8797 48.4014

-3.7276 41.5547

-3.5957 36.4226

-3.4792 32.4237

-3.3747 29.2018

-3.2213 25.0381

-3.0885 21.9244

-2.9712 19.5024

-2.8662 17.5534

-2.7129 15.0520

-2.5802 13.1808

-2.4631 11.7252

-2.3582 10.5537

-2.2075 9.0725

-2.0768 7.9594

-1.9612 7.0905

-1.8576 6.3894

-1.7120 5.5196

-1.5851 4.8600

-1.4725 4.3415

-1.3713 3.9212

-1.2787 3.5725

-1.1940 3.2809

-1.1159 3.0332

-1.0435 2.8200

-0.9761 2.6348

-0.9129 2.4723

-0.8536 2.3287

-0.7975 2.2008

-0.7445 2.0861

-0.6942 1.9828

-0.6463 1.8891

-0.6006 1.8039

-0.5569 1.7260

-0.5151 1.6545

-0.4750 1.5887

-0.4364 1.5278

-0.3993 1.4715

-0.3636 1.4191

-0.3290 1.3703

-0.2957 1.3247

-0.2634 1.2821

-0.2322 1.2420

-0.2019 1.2044

-0.1726 1.1690

-0.1441 1.1356

-0.1163 1.1040

-0.0894 1.0742

-0.0632 1.0458

-0.0495 1.0314

-0.0360 1.0173

-0.0227 1.0036

-0.0096 0.9903

>> plot(T1,Y1(:,1))

>> hold on

>> grid on

>> plot(T1,Y1(:,2))

>> axis([0 5 -10 10])

>> t = 0.01:0.001:5;

>> Y = log(t);

>> plot(t,Y)

>> plot(t,Y,'--g')

>> Y = 1./t;

>> plot(t,Y,'--y')

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